MATHEMATICAL SECTION. 53 
presented, however, are designed for much greater distances and 
for any spheroid, and would serve, if need ever arose, for comput- 
ing the shortest distance between any two points on the terrestrial 
spheroid no matter how remote. 
19TH MEETING. APRIL 29, 1885. 
The Chairman, Mr, G. W. Hitt, presided. 
Present, nineteen members and one guest. 
Minutes of the eighteenth meeting read and approved. 
Mr. A. Zriwer read a paper entitled 
ON GRASSMANN’S SYSTEM OF GEOMETRY. 
This paper will appear in full in the Annals of Mathematics, vol. 
2, Nos. 1 and 2. 
In reply to a question by Mr. Curtis as to whether Grassmann’s 
system could be advantageously substituted for the Cartesian sys- 
tem, Mr. Zrwet expressed the opinion that it could not be so sub- 
stituted in general, but that it might in certain special cases. 
Grassmann has not, said Mr. ZiwET, made applications of his 
method to astronomy, nor indeed does its value consist in its 
adaptability to the solution of special problems. But for present- 
ing general geometrical truths it appears superior to Hamilton’s 
methods, to which it is closely related and with which it might be 
advantageously joined. 
Mr. Haut remarked that he had seen planetary orbits worked 
out after Hamilton’s method by J. Willard Gibbs, but the process 
appeared rather more laborious than the usual Gaussian one. 
The labor of computation of results, Mr. Hitt remarked, was 
practically the same by all methods. By introducing the needful 
symbols the general expressions may be made exceedingly simple, 
but when the numerical work begins it will be found that after par- 
ing off more or less extraneous matter there still remains a central 
kernel or core of computation from which there is no escape by 
any method whatsoever. 
With this view Mr. R.S. Woopwarp heartily concurred, and 
added that the supreme test of the usefulness of such systems as 
